Complexity of Source-Sink Monotone 2-Parameter Min Cut
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Publication:6373334
DOI10.1016/J.ORL.2021.12.009zbMath1525.90411arXiv2107.09743MaRDI QIDQ6373334
Venus Lo, S. Thomas McCormick, Maxwell Allman
Publication date: 20 July 2021
Abstract: There are many applications of max flow with capacities that depend on one or more parameters. Many of these applications fall into the "Source-Sink Monotone" framework, a special case of Topkis's monotonic optimization framework, which implies that the parametric min cuts are nested. When there is a single parameter, this property implies that the number of distinct min cuts is linear in the number of nodes, which is quite useful for constructing algorithms to identify all possible min cuts. When there are multiple Source-Sink Monotone parameters and the vector of parameters are ordered in the usual vector sense, the resulting min cuts are still nested. However, the number of distinct min cuts was an open question. We show that even with only two parameters, the number of distinct min cuts can be exponential in the number of nodes.
Programming involving graphs or networks (90C35) Sensitivity, stability, parametric optimization (90C31) Deterministic network models in operations research (90B10)
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